Gravitational field strength (ratios)

A 6.2*10^2-kg satellite above Earth's surface experiences a gravitational field strength of magnitude 4.5-N/kg. Knowing the gravitational field strength at Earth's surface and Earth's radius, how far above Earth's surface is the satellite? (Use ratio and proportion.)

2. Relevant equations

Fg = (GMm)/r2
g = GM/r2
gE = 9.8-N/Kg
rE = 6.37*10^6-m

3. The attempt at a solution

gs/gE = rs2/rE2
rs= √((rE2gs)/gE)

and my answer comes out to be 4.3*10^6-m. But the answer at the back of the book is 3.0*10^6-m, what did I do wrong? Thanks